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数据处理：设计算法，再将算法转换为程序设计语言对应的程序

计算机不能分析问题并产生问题的解决方案，必须由人来分析问题、确定解决方案、编写程序，再让计算机执行">
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                <h2 id="程序设计的关键是什么？"><a href="#程序设计的关键是什么？" class="headerlink" title="程序设计的关键是什么？"></a>程序设计的关键是什么？</h2><p>数据表示：从问题抽象出数据模型，从机外表示转换为机内表示</p>
<p><img src="https://shierjinghuang.github.io/2021/10/28/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/%E6%95%B0%E6%8D%AE%E8%A1%A8%E7%A4%BA.png" alt="数据表示"></p>
<p>数据处理：设计算法，再将算法转换为程序设计语言对应的程序</p>
<p><img src="https://shierjinghuang.github.io/2021/10/28/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/%E6%95%B0%E6%8D%AE%E5%A4%84%E7%90%86.png" alt="数据处理"></p>
<p>计算机不能分析问题并产生问题的解决方案，必须由人来分析问题、确定解决方案、编写程序，再让计算机执行程序最终获得问题的解</p>
<p>利用计算机求解问题的一般过程？</p>
<p><img src="https://shierjinghuang.github.io/2021/10/28/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/%E8%AE%A1%E7%AE%97%E6%9C%BA%E8%A7%A3%E5%86%B3%E9%97%AE%E9%A2%98%E7%9A%84%E8%BF%87%E7%A8%8B.png" alt="计算机解决问题的过程"></p>
<p>本课程主要讨论非数值问题的数据组织和处理</p>
<p>（1）数据的逻辑结构：线性表、树、图等数据结构，其核心是如何组织待处理的数据以及数据之间的关系；</p>
<p>（2）数据的存储结构：如何将表、树、图等数据结构存储到计算机的存储器中，其核心是如何有效地存储数据以及数据之间的逻辑关系</p>
<p>（3）算法：如何基于数据的某种存储结构实现插入、删除、查找等基本操作，其核心是如何有效地处理数据；</p>
<p>（4）常用数据处理技术：查找技术、排序技术等。</p>
### 数据结构的基础概念

<p>数据：所有能输入到计算机中并能被程序识别和处理的符号集合</p>
<p><img src="https://shierjinghuang.github.io/2021/10/28/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/%E5%9B%BE%E7%89%871.png" alt="数据"></p>
<p>数据元素：数据的基本单位，在程序中作为一个整体进行考虑和处理，通常情况下，数据元素具有相同个数和类型的数据项。</p>
<p>数据项：构成数据元素的最小单位</p>
<p>数据结构：相互之间存在一定关系的数据元素的集合</p>
<p>数据的逻辑结构：数据元素之间逻辑关系的整体</p>
<p><img src="https://shierjinghuang.github.io/2021/10/28/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E7%9A%84%E5%88%86%E7%B1%BB.png" alt="数据结构的分类"></p>
<h3 id="数据的存储结构"><a href="#数据的存储结构" class="headerlink" title="数据的存储结构"></a>数据的存储结构</h3><p>数据的存储（物理）结构：数据及其逻辑结构在计算机中的表示</p>
<p>（1）顺序存储结构：用一组连续的存储单元依次存储数据元素，数据元素之间的逻辑关系由元素的存储位置表示</p>
<p>（2）链接存储结构：用一组任意的存储单元存储数据元素，数据元素之间的逻辑关系用指针来表示 </p>
<h3 id="抽象数据类型"><a href="#抽象数据类型" class="headerlink" title="抽象数据类型"></a>抽象数据类型</h3><p>抽象数据类型：一个数据模型以及定义在该模型上的一组操作 </p>
<p><img src="https://shierjinghuang.github.io/2021/10/28/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/%E5%AE%9E%E7%8E%B0%E6%8A%BD%E8%B1%A1%E6%95%B0%E6%8D%AE%E7%B1%BB%E5%9E%8B.png"></p>
<center>实现抽象数据类型</center>
## 算法及算法的特性

<p>算法 : 是对特定问题求解步骤的一种描述，是指令的有限序列</p>
<h4 id="算法的基本要求"><a href="#算法的基本要求" class="headerlink" title="算法的基本要求"></a>算法的基本要求</h4><p>（1）有穷性：总是在执行有穷步之后结束，且每一步都在有穷时间内完成</p>
<p>（2）确定性：每一条指令必须有确切的含义，相同的输入得到相同的输出</p>
<p>（3）可行性：操作步骤可以通过已经实现的基本操作执行有限次来实现</p>
<p><img src="https://shierjinghuang.github.io/2021/10/28/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/%E5%A5%BD%E4%BB%A3%E7%A0%81%E7%9A%84%E7%89%B9%E5%BE%81.png" alt="好代码的特征"></p>
<h2 id="算法分析"><a href="#算法分析" class="headerlink" title="算法分析"></a>算法分析</h2><p>算法分析：对已设计的算法，如何评价或判断其优劣</p>
<p>事后统计（定量分析）：将算法实现，测算其时间和空间开销</p>
<p>事前分析（定性分析）：对算法所消耗资源的一种估算方法</p>
<p>基本语句：执行次数与整个算法的执行次数成正比的操作指令</p>
<p>问题规模：输入量的多少</p>
<h3 id="算法的时间复杂度"><a href="#算法的时间复杂度" class="headerlink" title="算法的时间复杂度"></a>算法的时间复杂度</h3><p>时间复杂度：当问题规模充分大时，算法中基本语句的执行次数在渐近意义下的阶——关注的是增长趋势</p>
<p>定义1-1  若存在两个正的常数 c 和 n0，对于任意 n ≥ n0，都有T(n) ≤ c × f(n)，则称T(n) = O(f(n))。</p>
<p>T(n)和f(n)具有相同的增长趋势，T(n)的增长至多趋同于函数f(n)的增长</p>
<p><strong>Ο(1)＜(log2n)＜(n)＜(nlog2n)＜(n2)＜(n3)＜…＜(2n)＜(n!)</strong></p>
<p>时间复杂度是在不同数量级的层面上比较算法</p>
<h3 id="算法的空间复杂度"><a href="#算法的空间复杂度" class="headerlink" title="算法的空间复杂度"></a>算法的空间复杂度</h3><p>空间复杂度：算法在执行过程中需要的辅助空间数量</p>
<p>除算法本身和输入输出数据所占用的空间外，算法临时开辟的存储空间</p>
<p>空间复杂度也是问题规模的函数，通常记作：S(n) = O(f(n)) </p>
<p>就地（原地）算法：空间复杂度为O(1)，辅助空间是常数</p>
<p>定理1-1：若T(n) = amnm + am-1nm-1 +  + a1n + a0是一个m次多项式，则T(n) = O(nm)</p>
<p>分析的策略是从内部（或最深层部分）向外展开，分析的策略是设其执行次数为T(n)，则有2T(n) ≤ n，即T(n) ≤ log2n</p>
<p><img src="https://shierjinghuang.github.io/2021/10/28/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/%E9%80%92%E5%BD%92%E7%AE%97%E6%B3%95.png" alt="递归算法"></p>
<p>如果算法的时间代价与输入数据有关，则需要分析最好情况、最坏情况、平均情况</p>
<ol>
<li>最好情况：不能代表算法的效率，当出现概率较大时分析</li>
<li>最坏情况：最坏能坏到什么程度，实时系统需要分析</li>
<li>平均情况：已知输入数据分布情况，通常假设等概率分布</li>
</ol>
<h1 id="数据结构-第一章-绪论题目"><a href="#数据结构-第一章-绪论题目" class="headerlink" title="数据结构 第一章 绪论题目"></a>数据结构 第一章 绪论题目</h1><h3 id="判断题"><a href="#判断题" class="headerlink" title="判断题"></a>判断题</h3><ol>
<li>数据元素是数据的最小单位。  (F)</li>
<li> 数据的逻辑结构是指数据的各数据项之间的逻辑关系。 (F)</li>
<li> 数据结构概念包括数据之间的逻辑结构、数据在计算机中的存储方式和数据的运算三个方面。 (T)</li>
<li> 数据结构的抽象操作的定义与具体实现有关。 (F)</li>
<li> 算法和程序没有区别，在数据结构中二者是通用的。  (F)</li>
<li> 数据结构包括数据对象集以及它们的逻辑结构和物理结构，还包括与数据对象相关联的操作集，以及实现这些操作的高效的算法。  (T)</li>
</ol>
<h3 id="单选题"><a href="#单选题" class="headerlink" title="单选题"></a>单选题</h3><ol>
<li> 在 Data_Structure = (D，R)中，D 是（ ）的有限集合。  (A)</li>
</ol>
<p>   A 数据元素   B 算法  C   数据操作   D数据对象</p>
<ol start="2">
<li> 以下关于数据结构的说法中错误的是（ ）   (A)</li>
</ol>
<p>   A.数据结构相同，对应的存储结构也相同  B.数据结构涉及数据的逻辑结构存储结构和施加其上的操作3个方面</p>
<p>   C.数据结构操作的实现与存储结构有关    D.定义逻辑结构时可不考虑存储结构</p>
<ol start="3">
<li> 算法分析的目的是( )    (C)</li>
</ol>
<p>   A.找出数据结构的合理性                                  B.研究算法中的输入和输出的关系   </p>
<p>   C.分析算法的效率以求改进                              D.分析算法的易读性和文档性</p>
<ol start="4">
<li> 算法分析的两个主要方面是( )  (A)</li>
</ol>
<p>   A.空间复杂度和时间复杂度   B.正确性和简明性 C.可读性和文档性 D.数据复杂性和程序复杂性</p>
<ol start="5">
<li><p>采用链结构存储线性表时，其地址（ ）。</p>
</li>
<li><p> 一个正确的算法应该具有 5 个特性，除输入、输出特性外，另外 3 个特性是（ ）。  </p>
</li>
</ol>

                
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